Finding focus using synthetic star

[skybadger]

I am trying to find the actual back focus distance on my homemade RC without pointing at a real star and facing the problem that focusing on anything else results in focus at a significan distance from infinity focus. 

I had the bright idea of putting a synthetic star in the eyepiece next to a viewing hole and a large optical flat at the end of the scope. 

My thinking is that the point source, when at the infinity focus point, will be made parallel by the scope, which will reflect off the flat and come back to a focus at the viewing hole. If it's inside focus I think the telescope will present a convergent bean to the flat and it will come back as a donut. For outside focus, it will be convergent and also be a donut. Moving through actual focus will cause the image of the star to come to focus at the infinity position. 

Is this correct ? Is this the standard null test ? 

[vlaiv]

It will work in this arrangement:

Above is setup you are describing - telescope with eyepiece pointed at optical flat.

Bottom part of the image is eyepiece assembly enlarged. You need to fashion custom eyepiece in order for that to work. You need to bring source of light of artificial star at actual focal point of the eyepiece - at the field stop.

If you take standard optical cable thread to act as your artificial star - you need to route it inside eyepiece and make it end at field stop - pointing outside towards the telescope.

This way when you look at eyepiece and you are in focus - artificial star will be in focus as well.

If you want to DIY solution just for testing and we are not discussing novel device - there is much simpler solution for you to try.

You will need another scope, and by the looks of your signature - you will have at least one for this purpose (although even simple finder can do).

Here is diagram showing arrangement:

Take your second scope - put eyepiece inside - focus at infinity, take eyepiece out and put artificial star in at focus plane of that telescope.

Objective will then project parallel beam of light aimed at "infinity" - on the other side place your RC (it does not matter if projecting scope is smaller - just make their optical axis parallel - but you can aim at one half - say bottom of larger scope aperture) and it will receive light as if coming from infinity (light will be collimated).

Then you insert eyepiece and focus artificial star to a point. That will be your focus position.

Third option is to use "close" focus and calculate difference to focus position if you know focal length of your instrument.

Say your RC has FL of 2000mm. Put artificial star at 20m away.

It will then focus at

1/2000 = 1/20000 + 1/focus_position

1/2000 = focus_position + 20000 / (20000 * focus_position)

20000 * focus_position = 2000 * focus_position + 2000*20000

18000 * focus_position = 2000 * 20000

focus_position = 2000 * 20000/18000 = 2222.22mm - your actual focus will be 222.22mm inward from where you focused (you will focus at 2222.22 but your FL is 2000 so you will be 2222.22 - 2000 = 222.22mm out).

[skybadger]

I thought about the seconds scope but that requires you to have solved the same problem in the absence of stars -exactly knowing where infinity focus is. 

I also thought about the latter. Bringing objects closer from infinity it's possible to calculate the actual position of focus but it will be quite a way away and is hard to cobble together a set of extensions for and isn't a definitive yes/no I'm looking for. 

The ultimate aim is to set the viewpoint at the back focus distance and adjust the mirror separation to obtain focus. 

Cheers Vlav.

[vlaiv]

6 hours ago, skybadger said:

I also thought about the latter. Bringing objects closer from infinity it's possible to calculate the actual position of focus but it will be quite a way away and is hard to cobble together a set of extensions for and isn't a definitive yes/no I'm looking for. 

How about daytime focus at something very far away or perhaps using the Moon?

Using the same equation from above (1/f = 1/f1+1/f2) you can see how much back focus you need depending on distance.

Say you have something that is very far away - maybe 10Km. That should not move focus point too much.

focus_position = fl * distance/(distance-fl)

Say FL is 2 meters and distance is 10000m, in that case focus position will be 2 * 10000 / 9998 = 2000.4mm or just 0.4 away from where it is supposed to be.

You can also go the other way around and see what will effective FL be if you put focus position where you want it to be (thus missing by 0.4mm). Just solve for FL if you have distance and focus position.

[davidc135]

7 hours ago, skybadger said:

I thought about the seconds scope but that requires you to have solved the same problem in the absence of stars -exactly knowing where infinity focus is. 

I also thought about the latter. Bringing objects closer from infinity it's possible to calculate the actual position of focus but it will be quite a way away and is hard to cobble together a set of extensions for and isn't a definitive yes/no I'm looking for. 

The ultimate aim is to set the viewpoint at the back focus distance and adjust the mirror separation to obtain focus. 

Cheers Vlav.

But aren't back focus, focal length and residual spherical aberration in an RC all functions of mirror separation which is unknown if you wish to adjust it?

(If) the SA is significant for non optimal mirror separation a Ronchi ep could be used with a star whilst mirror separation wass adjusted. But perhaps any change in correction is small.

Or both focal position and correction could measured using the flat and a knife edge to null the return focus.

An autocollimating flat's departure from a true plane might affect focal position so it would need to be checked. I'm not sure what effect a 1/4 wave sag, for instance, would have.

If image quality is fine, wouldn't the moon be the easiest object?

David

Edited May 2, 2022 by davidc135

[skybadger]

Yes, but I need to get to a place to start from, where I know the infinity focus is the prescription distance behind the primary which I can then adjust if necessary using a ronchi to check.  The deviation from prescription should be small. You also incur spherical aberration for objects closer than infinity. 

This is all about getting to a starting point on the bench to setup for a night of checking and adjusting using the stars later, hopefully as little as possible.

It's a good point about using a point and a knife edge though. It comes back to whether I can position it on the optical axis well enough. 

Thanks

 

[davidc135]

Do you have a flat of comparable size? The 12.5'' RC should have enough room to accomodate the source and knife edge side by side whilst allowing a view of the whole aperture. If the flat is mounted on gimballs that helps with the fiddling around. A cube beamsplitter can be handy but not essential.

It may be that astigmatism due to miscollimation or separation of source and return focus is present but even so, I think SA can be judged independantly.

Below is a Foucaultgram of an 8'' sct just inside focus. It suffers from bad astigmatism but that hardly shows in the image.

David

[skybadger]

I have a 6" optical flat and a 12" plate blank which I can try with. 

[davidc135]

The 6'' flat is going to be too small and the blank too irregular to be helpful.

My plan would be:

Accurately establish the infinity focus of the 140mm refractor, without diagonal, using the sun's image (briefly) or a star. I used masking tape on a microscope slide in turn taped to a drawtube focused on the sun.

I would select 3 RC back focus positions bracketting the nominal design bf eg 8'' and say +/- 1''.

On the bench and using the 140 refractor as the source I would adjust the mirror separations required for each back focus.

For each bf Polaris can be viewed with the Ronchi ep showing three to five bands. Hopefully the range of settings will give results that show the optics moving from over-correction through correction to under-correction. Intrapolation (or extrapolation) will give the right back focus.

David

[skybadger]

I can do that. Good suggestions all round. 

Thanks for your input. I'll report back how I get on. Probably at the weekend.